According to the myths, Lady Sif was Thor's wife, with golden hair and eyes only for him.
The comic book version is a little more complicated. Her hair is black for starters—a trick played on her by Loki—and the love of her (immortal) life has other gals he sees, despite her clear and obvious adoration of him. Fifty years of comics leads to a lot of ups and downs like that.
For the movie, a certain amount of simplification is in order, with a lot of stuff left unsaid. They keep Sif's dark hair by not asking Noted Brunette Jaimie Alexander to get it dyed, and as for her romantic ties with Thor? They're reduced to some longing looks and the implication—never directly stated—that she and Thor once had a thing together. They go deeper into that in the sequel, Thor: The Dark World, but for now, we're left only with hints and suggestions.
We do know that she seems pretty much okay with it all: smiling and laughing with Thor and not letting him get away with taking too much credit while still staying friends. Just look at the first thing she says in the film:
THOR: And who proved wrong all who scoffed at the idea that a young maiden could be one of the fiercest warriors this Realm has ever known?
SIF: I did.
THOR: True, but I supported you!
Loyalty, in fact, is her main motivation here: backing Thor's play, whatever it may be and standing by him even when he gets exiled to Earth. She can spot Loki's jealousy, and smells a rat when he takes over, ensuring that Thor has someone minding the store in Asgard while he's off dealing with the whole "dad's mad at me" thing.
Eventually, she travels to Earth to bring him home, and even stands up to the Destroyer while Thor is still powerless in the big CGI finale:
SIF: No! I will die a warrior's death. Stories will be told of this day!
THOR: Live, and tell those stories yourself.
That makes her something of a sidekick to Thor, able to be there for everyone when he's distracted and lend him a hand when he needs it. Her ferocious loyalty to Thor means that she'll always have his back, and while we like our female characters to be their own heroes instead of playing second fiddle to the boys, we have to admit we're fond of this particular version: tough, brave, standing by her friends, and willing to do the right thing even when it gets you into trouble.
That makes her more of a hero than a sidekick in our book, and we're glad Thor gives her room to show everyone why.